by
Stewart, James; Redlin, Lothar; Watson, Saleem

Answer

(a) reflect $f(x)$ about the $x$ and $y$ axes, and shift up 1 unit
(b) reflect $f(x)$ about the $x$-axis, shrink vertically by $\frac{1}{5}$ and shift up 2 units

Work Step by Step

(a) We can obtain $1-f(-x)$ by reflecting the graph of $f(x)$ about the $x$-axis and $y$-axis and moving the graph up 1 unit.
(b) We can obtain $2-\frac{1}{5}f(x)$ by reflecting the graph of $f(x)$ about the $x$-axis, shrinking vertically by a factor of $\frac{1}{5}$ and shifting up 2 units.